There are 7 players who can play for a snooker team: Micky, Katie, Niles, Tommo, Paul, Jonno and Emma. Each week four players are needed to make up the team. One week, Micky and Katie are chosen for the team and the other two players are chosen at random. What is the probability that Niles is also in the team?

After Micky and Katie are chosen, the situation is: - Number of players remaining: 7 - 2 = 5 (Niles, Tommo, Paul, Jonno, Emma). - Number of team spots to fill: 4 - 2 = 2. We are choosing 2 players from the remaining 5. Each of the 5 players has an equal chance of being chosen. A simple way to think about this is that there are 2 available "winning" spots and 5 players competing for them. Therefore, the probability for any one player (like Niles) to be chosen is 2/5. More formally, using combinations: - The total number of ways to choose 2 players from the remaining 5 is "5 choose 2" or ⁵C₂ = (5!)/(2! * 3!) = 10. - The number of ways to choose Niles and one other player is "1 choose 1" (for Niles) multiplied by "4 choose 1" (for the other player), which is 1 * 4 = 4. - The probability is (Favourable outcomes) / (Total outcomes) = 4/10 = 2/5.